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3
votes
0answers
46 views

Estimate smooth vector, from dot-product queries

I have a secret $n$-dimensional vector $\mathbb{s} \in \mathbb{Z}^n$. I don't know $\mathbb{s}$; my goal is to estimate $\mathbb{s}$. I do have an oracle for the function $f_\mathbb{s} : \mathbb{Z}^...
5
votes
2answers
199 views

Lower bound proof for compressive sensing (Gel'fand widths)?

Let $x \in \mathbb{R}^n$ have $k$ non-zero entries. The main insight of compressive sensing is that there exist $m\times n$ matrices $A$ with $m = O(k \log n/k)$ such that any $x$ can be recovered ...
-3
votes
1answer
97 views

Proof of non-existence of the universal archiver? [closed]

Does anybody knows a proof that no algorithm $A$ exists that can reversibly transform every possible finite sequence $S$ to the sequence $C$ of smaller size? Here I assume $S$ and $C$ to be a finite ...
3
votes
0answers
77 views

Efficiently Detecting “edges” in the time frequency plane

Given a signal $y(t)\in\mathbb{R}$ I wish to detect edge patterns. $s(f,t)$ is a time-frequency decomposition of $y(t)$ in some window $(t-n,t+n)$ so that $f$ loosely corresponds to a local frequency....
0
votes
0answers
211 views

norms of compressible and incompressible vector

Let $a$ be a vector in $R^m$, such that $\sum_{i=1}^ma_i=0$ I would like to bound $\sqrt{2m(2m-1)}\|a\|_{\infty}$ by $\sqrt{2m}\|a\|_2$ (or other way arround with the sharp constants), in the case ...
11
votes
0answers
587 views

Complexity of finding the leading eigenvector of a graph Laplacian

Let ${\bf L}$ be the $n\times n$ Laplacian of a graph. What is the worst case complexity for calculating the maximum eigeinvector of ${\bf L}$? Are there any families of Laplacians for which it takes ...
17
votes
0answers
328 views

complexity of checking if a subspace is a Euclidean section of L1

If $X$ is a linear subspace of ${\mathbb R}^n$, $X$ is high-dimensional, and for every $x\in X$ we have $(1-\epsilon) \sqrt n ||x||_2 \leq ||x||_1 \leq \sqrt n ||x||_2$ for some small $\epsilon >...
1
vote
2answers
282 views

Complexity of Smoothed $\ell_0$ algorithm

I wanted to compute the complexity of a smoothed $\ell_0$ algorithm in BigO notation. The algorithm can be found here. Can anybody help me in this regard?
20
votes
6answers
1k views

Analogs of compressed sensing

In compressed sensing, the goal is to find linear compression schemes for huge input signals that are known to have a sparse representation, so that the input signal can be recovered efficiently from ...